Forgive me, because I am speaking from semi-ignorance on this. I haven't stayed at the HR Dongguan yet as I have typically stayed at other hotels in the area. But, I its definitley been on my radar for one of my upcoming trips.
It seems liee there has to be better transport solutions from HK to the HR DG than shuttles. In general, I try to avoid road transportwhen in SZ or DG as I have wasted too many hours of my life sitting in traffic there.
I have two suggestions that I think would make it easier.
1 - The easiest method I've found for the area - Take the KCR East Rail from Hung Hom Station in Kowloon to the SZ border at Lowu. Walk across the border and then use the Shenzhen-Guangzhou train. The train leaves every ~20 min all day long. You could take the train to either Zhangmoutou, the first stop (~20min trip/40RMB) and take a taxi from there, or to Shilong (closer to the HR DG) and take a taxi from there.
In general, this train is great for most of the industrial areas. I use it regularly to Zhangmutou adn to Guangzhou East station, which incidentally is pretty close to the GH Guangzhou.
2 - Less transfers, but pricier and probably slower - Take the Kowloon - Guangzhou Intercity train from Hung Hom Station in Kowloon to Dongguan/Changping station. Cost is ~145RMB and then take a taxi from there to the HR DG. The benefit is that you don't need to transfer at the border.